For what value of c does the following system not have a solution.
1/2x+1/5y=2
5x+2y=c
Answers
Answer:
The answer is 3. 1. There is '0' point of intersection, that means they do not intersect. This only possible when the lined are parallel to each other.
'c' can be any real number except 4 for which the considered system would have no solution.
When does a system of linear equation have no solution?When both the lines(represented by both the equations) are parallel and not coincident, then that system of linear equations have no solutions as there is no common point on both line.
If they are coincident (lying over each other), then there will have infinite solution since in that case, they will have infinite points in common.
Thus, if two lines are not in any of above case, they intersect at single point and in that case, the considered system of equation has unique single solution.
How to get the slope intercept form of a straight line equation?If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
[tex]y = mx +c[/tex]
Parallel lines(non-coincident) have same slope but different y-intercept.
Converting these equations to slope-intercept form, we get:
For first line:
[tex]\dfrac{1}{2}x + \dfrac{1}{5}y = 2\\\\ \dfrac{1}{5}y = 2 - \dfrac{1}{2}x\\\\y = 10 - \dfrac{5}{2}x\\\\y = -\dfrac{5}{2}x + 2[/tex]
and
For second line:
[tex]5x + 2y = c\\\\y = \dfrac{1}{2}c - \dfrac{5}{2}x\\\\y = -\dfrac{5}{2}x + \dfrac{c}{2}[/tex]
For no-solution, we need both lines to stay parallel but not coincident so that there is no common point (solution of this system) between those two lines.
Thus, we get:
[tex]2 \neq \dfrac{c}{2}\\\\\text{Multiplying 2 on both the sides}\\\\c \neq 4[/tex]
Since 'y' assumes real numbers assumingly, so 'c' can be any real number except 4 for which the considered system would have no solution.
Below is image attached of those parallel lines when c = 10.
Thus, 'c' can be any real number except 4 for which the considered system would have no solution.
Learn more about the case of 'no solution' here:
https://brainly.com/question/26254258
Related Questions
A=27 inches and b=36 inches what is the length of the hypotenuse
Answers
Answer:
Hypotenuse = 45 inches
Step-by-step explanation:
Let the hypotenuse be known as "C".
Definition of hypotenuse:
The hypotenuse is the longest side in a right triangle.
Since the word "hypotenuse" is stated in the question, we can assume that the triangle is a right triangle and therefore, Pythogoras theorem can be used to determine the measure of the hypotenuse.
Pythogoras theorem
x² = y² + z²[Where "x" is the hypotenuse, "y" and "z" are the legs of the right triangle].
We are given that:
Leg A = y = 27 inchesLeg B = z = 36 inchesHypotenuse = x = C inchesWhen the meausures are substituted in the formula, we get;
⇒ (C)² = (27)² + (36)²Evaluate the squares on the right hand side:
⇒ (C)² = (27)² + (36)²⇒ (C)² = 729 + 1296Simplify the expression on the right hand side:
⇒ (C)² = 729 + 1296⇒ (C)² = 2025Take square root both sides of the equation:
⇒ √(C)² = √2025⇒ C = 45 inchesTherefore, the measure of the hypotenuse is 45 inches.
Learn more about Pythogoras theorem: https://brainly.com/question/19859661
-4K2 – 8k – 3 =-3 – 5K2
Solve by factoring
Answers
Answer:
k = 0 or 8
Step-by-step explanation:
First, get the variables and constants on their side.
-4k^2 + 5k^2 - 8k = -3 + 3 Now simplify
k^2 - 8k = 0 Factor
k(k - 8) = 0 Solve
k = [0, 8]
If you want you can double check your answer by plugging in the values you got. First, 0.
0 - 0 - 3 = -3 - 0
-3 = -3. That works, so we know 0 is correct. Now 8
-4(64) - 8(8) - 3 = -3 - 5(64)
-256 - 64 - 3 = -3 - 320
-320 - 3 = -323
-323 = -323 That also works, so we know 8 is correct.
If you could body swap with any person for 24 hours, who would you choose?
Answers
Answer:
Chris evans
Step-by-step explanation:
what's the algebra meaning?
Answers
Answer:
the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Step-by-step explanation:
A student is trying to solve the system of two equations given below: equation p: a b = 6 equation q: 4a 2b = 19 which of the following steps can be used to eliminate the a term? −1(4a 2b = 19) −4(4a 2b = 19) −4(a b = 6) 4(a b = 6)
Answers
We will use the steps that can be used to eliminate the a term that will be -4(a+b=6). Option C is correct.
What is the system of two equations?A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.
The given equation in the problem is;
Equation P: a + b = 6
Equation Q: 4a + 2b = 19
To cancel out the equation q from the equation p.In order to cancel, the term of we has to multiply the term -4 in the equation p.
Hence we will use the steps that can be used to eliminate the a term that will be -4(a+b=6). Option C is correct.
To learn more about the system of two equations refer to the link;
https://brainly.com/question/21620502
Find the radius of a circle with an area of 89 square feet.
Answers
Answer:
[tex]r = 5.32\ feet[/tex]
Step-by-step explanation:
Step 1: Determine the radius
Formula to get the area of a circle → [tex]A=\pi r^2[/tex]
Insert 89 into the A and solve for r
[tex]\frac{89}{\pi} = \frac{\pi r^2}{\pi}[/tex]
[tex]28.3296 = r^2[/tex]
[tex]\sqrt{28.3295} = \sqrt{r^2}[/tex]
[tex]r = 5.32[/tex]
Answer: [tex]r = 5.32\ feet[/tex]
HELP A S A P ONLY CORRECT ANSWE
Answers
Answer:
the answer should be d
Step-by-step explanation:
you just have to multiply the per pound amount (1.29) by by the pound amount (5) and then you get your answer $6.45!
i hope this helps :)
Which expression gives the volume of a sphere with radius 17?
A. 4pi(17^3)
B. 4/3pi(17^2)
C. 4pi(17^2)
D. 4/3pi(17^3)
Answers
Answer:
D
Step-by-step explanation:
The formula for a sphere is 4(π/3) * r ^ 3. If we plug in r we get 17^3 * 4/3 * π
Write the slope-intercept form of equation.
1) 3x – 2y = -12
Answers
Answer:
[tex]y=\dfrac{3}{2}x+6[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slopeb is the y-interceptGiven equation:
[tex]3x-2y=-12[/tex]
To write the given equation in slope-intercept form, apply arithmetic operations to isolate the variable y.
Add 2y to both sides:
[tex]\implies 3x-2y+2y=-12+2y[/tex]
[tex]\implies 3x=2y-12[/tex]
Add 12 to both sides:
[tex]\implies 3x+12=2y-12+12[/tex]
[tex]\implies 3x+12=2y[/tex]
Switch sides:
[tex]\implies 2y=3x+12[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{2y}{2}=\dfrac{3x+12}{2}[/tex]
[tex]\implies \dfrac{2y}{2}=\dfrac{3x}{2}+\dfrac{12}{2}[/tex]
[tex]\implies y=\dfrac{3}{2}x+6[/tex]
Therefore, the slope-intercept form of the given equation is:
[tex]y=\dfrac{3}{2}x+6[/tex]
where 3/2 is the slope, and 6 is the y-intercept
Learn more about Slope-intercept form here:
https://brainly.com/question/27926846
Slope intercept form y=mx+b
Let's find
3x-2y=-123x+12=2yy=3/2x+12/2y=3/2x+6Done!
ILL GIVE BRAINLIEST
Using pi as 3.14. what is the circumference of a circle with a radius of 3mm.
Answers
Answer:
18.8
Step-by-step explanation:
Circumference
2πr2π(3)6π18.8mm²If A=3x^2 + 5x -6 and B= -2x^2 - 6x +7, then A-B equals ?
Answers
Answer:
5x^2 + 11x - 13 = A - B
Step-by-step explanation:
A - B = ? Substitute 3x^2 + 5x - 6 for A and - (-2x^2 - 6x + 7) for -B:
3x^2 + 5x - 6 - (-2x^2 - 6x + 7). or
3x^2 + 5x - 6 + 2x^2 + 6x - 7, or (after combining like terms):
5x^2 + 11x - 13 = A - B
solve the equation x+2=5x-2
Answers
Hey there!
Solve the equation:
Answer :x = 1 ✅
Explanations:x + 2 = 5x - 2
>> Add 2 to both sides
x + 2 + 2 = 5x - 2 + 2
x + 4 = 5x
>> Substract x from each side
x + 4 - x = 5x - x
4 = 4x
4x = 4
>> Divide both sides by 4
4x/4 = 4/4
x = 1
More about equations :
https://brainly.com/question/27436957
Have a good day ;)
Given :-
X + 2 = 5X - 2To find :-
The value of Xsolution:-
x + 2 = 5x -2
moving like terms to the same side2+2 = 5x - x
4 = 4x
1 = x
Complete the table.
f(a) = -3a2 + 10
-1
0
1
2
Answers
0 | 10
1 | 4
2 | -2
I need help, I can't do this exercise
Answers
Answer:
149 Degrees
Step-by-step explanation:
The angle 31 is marked for you on the figure, there is also a secondary angle marked on the other line parallel to the first. Since they are marked the same, the value of both must be 31 degrees, you can also prove this in a longer method by calculating the exact angle measures of each line. Now we simply simplify our basic equation.
180-31=x
149=x
Cleveland and his family are on a road trip. If they have traveled 1/2 of the total distance in the past 4 days, what fraction of the total distance did when they travel per day?
Answers
Answer:
1/8
Step-by-step explanation:
What is the area of the triangle?
Will mark brainlyest!!
Answers
Answer:
A = 28 sq cm
Step-by-step explanation:
Area of a triangle:
A = 1/2• base•height
= 1/2•7•8
= 28 sq cm
What is 4/5 in a percent
Answers
Answer:
80%
Step-by-step explanation:
I use cross multiplication for this
4/5 = ?/100
so you would do (4*100)/5 to get the percent which would then be 80%
The function f(x)=2^x and g(x)=f(x)+k. if k=2, what can be concluded about the graph?
the graph of g(x) is shifted vertically...
The graph ig g(x) si shifted horizontally
Answers
Answer:
Its shifted verticlly 2 and to the left 2.
Step-by-step explanation:
Its verticlly because when it says 2^x its going up if it said -2^x it would go down.
It goes left because it is 2^x=? so if you put it on the other side its negative which makes it to the left.
Golf Federation wants to find out which brand of golf balls are the most popular among men living in the United States between the ages of 25 and 40. They surveyed 100 of their male customers living in California between the ages of 25 and 40. The Golf Federation and found that the most popular golf ball is Miller followed by Smith and Sixon. Therefore, the Golf Federation concludes that the most popular brand of golf balls among men living in the United States between the ages of 25 and 40 is Miller. Select the statement that is true about Golf Federation's conclusion. A. The Golf Federation's conclusion was not valid because the sample was biased since all the male customers were of ages from 25 and 40. B. The Golf Federation's conclusion was not valid because the sample was biased since the male customers all lived in California. C. The Golf Federation's conclusion was valid because the sample was random. D. The Golf Federation's conclusion was valid because the sample was biased since the male customers all lived in California.
Answers
Using sampling concepts, it is found that the correct option is given by:
B. The Golf Federation's conclusion was not valid because the sample was biased since the male customers all lived in California.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, the objective is to make an estimate about the most popular brand of golf ball from men all over the United States, however, only customers from California were chosen, hence the sample is not representative and option B is correct.
More can be learned about sampling concepts at https://brainly.com/question/25122507
Answer:b
Step-by-step explanation:The Golf Federation's conclusion was not valid because the sample was biased since the male customers all lived in California.
Give a rule for a transformation that would be a rigid motion. Explain why your transformation would be a rigid motion.
Answers
Evaluate. Pre algebra
Answers
Answer:
[tex]4^3 =64\\\\(-3)^4 = 81[/tex]
Step-by-step explanation:
[tex]4^3 = 4\times 4 \times 4 = 64\\\\(-3)^4 = (-1)^4\cdot 3^4 = 81[/tex]
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Answer:
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Answer:
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Answer:
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Answer:
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Step-by-step explanation:
Lines p and q are parallel.
Parallel lines p and q are cut by transversals r and s. At the intersection of lines p, r, and s, clockwise from top left, the angles are blank, 93 degrees, blank, blank, 1, 60 degrees. At the intersection of lines q and s, the angles are blank, 2, blank, blank. At the intersection of r and q, the angles are 3, blank, blank, blank.
What is the measure of angle 2 in degrees?
27°
33°
60°
93°
Answers
Answer:
60°
Step-by-step explanation:
The given 60° angle and angle 2 are alternate interior angles of parallel lines p and q with transversal s, so they are congruent.
m<2 = 60°
Answer:
Based on the alternate interior angle theorem, the measure of angle 2 in the diagram given is: C. 60°
What is the Alternate Interior Angles Theorem?
The alternate interior angle theorem states that the measure of two alternate interior angles are congruent.
Angle 2 and 60° are alternate interior angles, therefore:
Angle 2 = 60° [alternate interior angle theorem].
Learn more about the alternate interior angle theorem on:
brainly.com/question/24839702
Step-by-step explanation:
Need help asap please
Answers
Answer:
9:49 is the answer because question say ratio is square of small and big
I need help
Solve for x
Answers
Answer:
x = 21
Step-by-step explanation:
5x + 15 = 2x + 78
3x = 63
x = 21
Answer:
x = 21°
Step-by-step explanation:
As corresponding angles in parallel lines are equal,
5x + 15 = 2x + 78
And now let us solve for x.
5x + 15 = 2x + 78
5x + 15 - 2x = 78
3x + 15 = 78
3x = 78 - 15
3x = 63
Divide both sides by 3.
x = 21°
PLS I NEED HELP I NEED TO UNDERSTAND
Answers
Answer:
you got incorrect before Imao hm whats the question?
Step-by-step explanation:
Are 2b + b and 3b equivalent expressions?
Answers
Moreover , they are equal too since on adding " 2b and b " we get 3b which is the other expression.
Answer:
the answer is yes
Step-by-step explanation:
yes it is an equivalent expression because 2b+b and 3b have the same value and length or numerator which equals yes.
A jug contains 2 gallons of water how Amy quarts of water does the jug contain
Answers
What does this mean pls help me I am gonna get a zero
Answers
Answer:
36 monkeys where sleeping
What is the solution to the equation below? In X = 2.1
Answers
Answer:
log(b) x = y is the same and saying b^y = x
so 6^2.1 = x
x = 43.06
Step-by-step explanation: